Gasification effects in the heterogeneous ignition of a condensed fuel by a hot gas

An analysis is presented to describe the heterogeneous ignition of a condensed fuel suddenly exposed to a hot oxidizing atmosphere. The exothermic heterogeneous reaction, generating gaseous products, is considered to be of the Arrhenius type with an activation energy large compared with the initial thermal energy of the fuel. Instantaneously after contact with the gases the surface temperature rises to a jump value which is calculated allowing for variable transport properties of fuel and gas. The effect of the chemical heat release and the cooling effect due to the gasification flow are taken into account in obtaining an integral equation, involving a single parameter Δ, which is solved to describe the evolution of surface temperature with time. A runaway in surface temperature is found to occur at a well defined ignition time, which is calculated as a function of Δ. For values of Δ above a critical value no ignition occurs because the cooling effects of the gasification flow dominate over the effects of chemical heat release.